Multivariate Asymmetric GARCH Model with Dynamic Correlation Matrix

Abstract

This study examines the problem of modeling the joint dynamics of conditional volatility of several financial assets under an asymmetric relationship between volatility and shocks in returns (leverage effect). We propose a new multivariate asymmetric conditional heteroskedasticity model with a dynamic conditional correlation matrix (DCC-EGARCH). The proposed method allows modelling the joint dynamics of several financial assets taking into account the leverage effect in the financial markets. DCC-EGARCH model has two main advantages over previously proposed multivariate asymmetric specifications. It involves a substantially simpler optimization problem and does away with the assumption of conditional correlation time invariance. These features make the model more suitable for practical applications.To study the properties of the obtained estimators,we conducted a simulated data analysis. As a result, we found statistical evidence in favor of the developed DCC-EGARCH model compared with the symmetric DCC-GARCH process in case of considering data with the presence of the leverage effect. Further, we applied the proposed method to analyze the joint volatility of Rosneft stock returns and Brent oil prices. By estimating the DCC-EGARCH model, we found statistical evidence for both the presence of the leverage effect in the oil price data and the presence of the dynamic correlation structure between the time series, which motivates the practical application of the proposed method.